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Sequential Monte Carlo Samplers are a class of stochastic algorithms for Monte Carlo integral estimation w.r.t. probability distributions, which combine elements of Markov chain Monte Carlo methods and importance sampling/resampling…

Probability · Mathematics 2007-05-23 Andreas Eberle , Carlo Marinelli

We present an adaptive multilevel Monte Carlo (AMLMC) algorithm for approximating deterministic, real-valued, bounded linear functionals that depend on the solution of a linear elliptic PDE with a lognormal diffusivity coefficient and…

Numerical Analysis · Mathematics 2022-12-07 Joakim Beck , Yang Liu , Erik von Schwerin , Raúl Tempone

Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, the exact sampling…

Statistics Theory · Mathematics 2018-11-05 Avetik Karagulyan

We investigate Monte Carlo based algorithms for solving stochastic control problems with probabilistic constraints. Our motivation comes from microgrid management, where the controller tries to optimally dispatch a diesel generator while…

Optimization and Control · Mathematics 2024-02-06 Alessandro Balata , Michael Ludkovski , Aditya Maheshwari , Jan Palczewski

Discrete time stochastic optimal control problems and Markov decision processes (MDPs), respectively, serve as fundamental models for problems that involve sequential decision making under uncertainty and as such constitute the theoretical…

Optimization and Control · Mathematics 2023-03-08 Christian Beck , Arnulf Jentzen , Konrad Kleinberg , Thomas Kruse

We provide an a priori analysis of collocation methods for solving elliptic boundary value problems. They begin with information in the form of point values of the data and utilize only this information to numerically approximate the…

Numerical Analysis · Mathematics 2025-01-08 Andrea Bonito , Ronald DeVore , Guergana Petrova , Jonathan W. Siegel

Importance sampling is a Monte Carlo method which designs estimators of expectations under a target distribution using weighted samples from a proposal distribution. When the target distribution is complex, such as multimodal distributions…

Methodology · Statistics 2026-02-04 Anas Cherradi , Yazid Janati , Alain Durmus , Sylvain Le Corff , Yohan Petetin , Julien Stoehr

This paper introduces a Monte Carlo method for maximum likelihood inference in the context of discretely observed diffusion processes. The method gives unbiased and a.s.\@ continuous estimators of the likelihood function for a family of…

Statistics Theory · Mathematics 2009-03-03 Alexandros Beskos , Omiros Papaspiliopoulos , Gareth Roberts

This article presents a novel approach, named MCMP (Monte Carlo Motion Planning), to the problem of motion planning under uncertainty, i.e., to the problem of computing a low-cost path that fulfills probabilistic collision avoidance…

Robotics · Computer Science 2015-06-01 Lucas Janson , Edward Schmerling , Marco Pavone

A numerical technique is introduced that reduces exponentially the time required for Monte Carlo simulations of non-equilibrium systems. Results for the quasi-stationary probability distribution in two model systems are compared with the…

Adaptation and Self-Organizing Systems · Physics 2009-11-07 A. Bandrivskyy , S. Beri , D. G. Luchinsky , R. Mannella , P. V. E. McClintock

This paper is on Bayesian inference for parametric statistical models that are defined by a stochastic simulator which specifies how data is generated. Exact sampling is then possible but evaluating the likelihood function is typically…

Machine Learning · Statistics 2020-03-02 Borislav Ikonomov , Michael U. Gutmann

The problem of estimating the probability p=P(g(X<0) is considered when X represents a multivariate stochastic input of a monotone function g. First, a heuristic method to bound p is formally described, involving a specialized design of…

Statistics Theory · Mathematics 2015-03-17 Nicolas Bousquet

In this article we revisit the problem of numerical integration for monotone bounded functions, with a focus on the class of nonsequential Monte Carlo methods. We first provide new a lower bound on the maximal $L^p$ error of nonsequential…

Numerical Analysis · Mathematics 2024-01-05 Subhasish Basak , Julien Bect , Emmanuel Vazquez

In this work, we propose a smart idea to couple importance sampling and Multilevel Monte Carlo (MLMC). We advocate a per level approach with as many importance sampling parameters as the number of levels, which enables us to compute the…

Probability · Mathematics 2017-07-10 Ahmed Kebaier , Jérôme Lelong

This paper sets up a methodology for approximately solving optimal investment problems using duality methods combined with Monte Carlo simulations. In particular, we show how to tackle high dimensional problems in incomplete markets, where…

Computational Finance · Quantitative Finance 2013-05-16 L C G Rogers , Pawel Zaczkowski

We consider the probabilistic numerical scheme for fully nonlinear PDEs suggested in \cite{cstv}, and show that it can be introduced naturally as a combination of Monte Carlo and finite differences scheme without appealing to the theory of…

Probability · Mathematics 2010-08-26 Arash Fahim , Nizar Touzi , Xavier Warin

We report multipronged progress on the stochastic averaging approach to numerical analytic continuation of quantum Monte Carlo data. With the sampled spectrum parametrized with delta-functions in continuous frequency space, a calculation of…

Strongly Correlated Electrons · Physics 2023-01-11 Hui Shao , Anders W. Sandvik

We develop a pure Monte Carlo method to compute $E(g(X_T))$ where $g$ is a bounded and Lipschitz function and $X_t$ an Ito process. This approach extends a previously proposed method to the general multidimensional case with a SDE with…

Probability · Mathematics 2016-07-18 Mahamadou Doumbia , Nadia Oudjane , Xavier Warin

We consider penalized extremum estimation of a high-dimensional, possibly nonlinear model that is sparse in the sense that most of its parameters are zero but some are not. We use the SCAD penalty function, which provides model selection…

Econometrics · Economics 2024-02-23 Joel L. Horowitz , Ahnaf Rafi

Problems with topological uncertainties appear in many fields ranging from nano-device engineering to the design of bridges. In many of such problems, a part of the domains boundaries is subjected to random perturbations making inefficient…

Numerical Analysis · Mathematics 2020-08-25 Viktor Reshniak , Yuri Melnikov